Severely disabled people will be worse off by £500 a year under "nasty" Thatcherite cuts to benefits, the shadow work and pensions secretary, Yvette Cooper, warned.

Families with young children will also suffer a heavy hit, she said, raising questions about David Cameron's pledge to lead the most family friendly government in Europe as tax credits are reduced and child benefit is frozen.

Cooper criticised George Osborne today after the chancellor declared that Britain's record fiscal deficit could not be tackled unless "lasting welfare reform" is introduced.

Osborne announced £11bn of savings by 2014-15:

• With the exception of state pension and pension credit, benefits will rise next year in line with the consumer prices index (CPI) rather than the retail prices index (RPI). This will save £6bn a year by the end of the parliament. The CPI is lower than the RPI because it does not include housing costs.

• Child benefit, which will rise in line with the CPI, will be frozen for three years.

• The cost of housing benefit will be cut by 7%, or £1.8bn, by introducing maximum limits, among other changes.

• People claiming the disability living allowance (DLA), which costs £11bn, will have to undergo a medical assessment in 2013.

• The "poorly targeted" health in pregnancy grant will be abolished from April next year, and Sure Start maternity grants will be restricted to the first child only.

Cooper said the changes will lead to a £130 cut in the value of child benefit and a £500 cut for severely disabled people. The change in benefit upratings from RPI to CPI means severely disabled people will lose £285 from the disability living allowance and £235 from the employment and support allowance by 2014.

"Someone who is severely disabled will not only have their benefits cut by this," Cooper said. "Housing benefit will also only be uprated by CPI rather than going up in line with rent. So you could very quickly find yourself not being able to pay your rent as well."

Cooper said families would face overall cuts of £3bn. "It is a heavy hit to families with young children in particular. It gives the lie to the Tories' promise to be the most family friendly government ever.

"When you take account of the additional VAT as well as the cuts to tax credits – families with a joint income of over £30,000 a year are being hit – and the cuts to child benefit, it is a big drop overall in support for children. That is deeply unfair. We should be investing in our future, not cutting back support."

Labour was also critical of a little-noticed aspect of the budget red book: more people will have higher marginal deduction rates (MDRs). The red book shows that a higher number of low earners will take home less pay as a result of the budget changes.

Cooper said: "For all [the work and pensions secretary] Iain Duncan Smith's talk of improving work incentives, they have actually cut the incentives and they are cutting support for people.

"They have already cut help for people to get back into work. Now they are cutting help for people who can't work as well. This is even before they are hit with VAT increases.

"So families on the very lowest incomes are going to be hit with cuts in support and increases in VAT. It is deeply unfair. It is a return to the kind of Thatcherite, nasty approach of the 1980s which they told us they'd turned their backs on."

The lone-parent charity Gingerbread said families with young children would soon feel the pain of the budget. Fiona Weir, chief executive, said: "A family having a second child could be over £1,200 worse off this year. These cuts will really hit families with young children hard."